Kierkegaard was not an advocate for traditional apologetic methodology. Instead, he used a Socratic dialectic approach in order to present a particular case. As we will be discussing here that case is the problem of Evil.
To be blunt there is no problem of evil in the eyes of Kierkegaard. To relate the problem of evil to the existence of God is like comparing apples and oranges. Why is there any sort of problem as it relates to evil? In what world does the aforementioned problem go to the existence of being? How is a divine mind or consciousness related to the problem? In Kierkegaard’s mind, it’s not entirely clear how any of these events are related to existence.
Therefore, the answer to the proposed question is simple for Kierkegaard. Assuming that the problem indeed is able to render God as non-existent (which is a premise he does not hold), then what of evil? does it in someway disappear as a problem now that you have rendered God non-existent? By no means! We are still left with the same problem. This means either the nature of the question is incorrectly stated; or more likely, the nature of the question has nothing to do with existence.
Again, like many other times, we have witnessed the genius of Kierkegaard. Namely, the ability he has to answer a profound question, with a profoundly simple answer.